8. The expected value of a distribution is not always finite. It could be infinite, or it might not exist at all (think [infinity]−[infinity] ). When the expected value fails to be finite, what does this have to do with the shape of the distribution? 9. Do all random variables posses a moment-generating function? Why or why not? 10. Let X be an absolutely continuous random variable with density function f, and let Y=g(X) be a new random variable that is created by applying some transformation g to the original X. If all I care about is the expected value of Y, must I first derive the entire distribution of Y (using the CDF method, the transformation formula, MGFs, whatever) in order to calculate it? If so, why? If not, what can I do instead?